LMFDB - Embedded newform 490.3.f.f.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,3,Mod(197,490)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("490.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			393.2
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	490.393
Dual form			490.3.f.f.197.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.15831 + 1.15831i) q^{3} -2.00000i q^{4} +(-1.81662 + 4.65831i) q^{5} -2.31662 q^{6} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.15831 + 1.15831i) q^{3} -2.00000i q^{4} +(-1.81662 + 4.65831i) q^{5} -2.31662 q^{6} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +(-2.84169 - 6.47494i) q^{10} +0.683375 q^{11} +(2.31662 - 2.31662i) q^{12} +(-11.9499 - 11.9499i) q^{13} +(-7.50000 + 3.29156i) q^{15} -4.00000 q^{16} +(-23.7916 + 23.7916i) q^{17} +(6.31662 + 6.31662i) q^{18} -9.63325i q^{19} +(9.31662 + 3.63325i) q^{20} +(-0.683375 + 0.683375i) q^{22} +(-17.1082 - 17.1082i) q^{23} +4.63325i q^{24} +(-18.3997 - 16.9248i) q^{25} +23.8997 q^{26} +(17.7414 - 17.7414i) q^{27} +16.5330i q^{29} +(4.20844 - 10.7916i) q^{30} +23.8496 q^{31} +(4.00000 - 4.00000i) q^{32} +(0.791562 + 0.791562i) q^{33} -47.5831i q^{34} -12.6332 q^{36} +(18.5752 - 18.5752i) q^{37} +(9.63325 + 9.63325i) q^{38} -27.6834i q^{39} +(-12.9499 + 5.68338i) q^{40} +0.200503 q^{41} +(-41.1161 - 41.1161i) q^{43} -1.36675i q^{44} +(29.4248 + 11.4749i) q^{45} +34.2164 q^{46} +(-33.7916 + 33.7916i) q^{47} +(-4.63325 - 4.63325i) q^{48} +(35.3246 - 1.47494i) q^{50} -55.1161 q^{51} +(-23.8997 + 23.8997i) q^{52} +(-65.9578 - 65.9578i) q^{53} +35.4829i q^{54} +(-1.24144 + 3.18338i) q^{55} +(11.1583 - 11.1583i) q^{57} +(-16.5330 - 16.5330i) q^{58} -23.1003i q^{59} +(6.58312 + 15.0000i) q^{60} -12.1662 q^{61} +(-23.8496 + 23.8496i) q^{62} +8.00000i q^{64} +(77.3747 - 33.9578i) q^{65} -1.58312 q^{66} +(0.992064 - 0.992064i) q^{67} +(47.5831 + 47.5831i) q^{68} -39.6332i q^{69} +63.2665 q^{71} +(12.6332 - 12.6332i) q^{72} +(33.3087 + 33.3087i) q^{73} +37.1504i q^{74} +(-1.70844 - 40.9169i) q^{75} -19.2665 q^{76} +(27.6834 + 27.6834i) q^{78} -112.266i q^{79} +(7.26650 - 18.6332i) q^{80} -15.7494 q^{81} +(-0.200503 + 0.200503i) q^{82} +(23.1161 + 23.1161i) q^{83} +(-67.6082 - 154.049i) q^{85} +82.2322 q^{86} +(-19.1504 + 19.1504i) q^{87} +(1.36675 + 1.36675i) q^{88} -79.8496i q^{89} +(-40.8997 + 17.9499i) q^{90} +(-34.2164 + 34.2164i) q^{92} +(27.6253 + 27.6253i) q^{93} -67.5831i q^{94} +(44.8747 + 17.5000i) q^{95} +9.26650 q^{96} +(-50.6834 + 50.6834i) q^{97} -4.31662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 6 q^{5} + 4 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 6 * q^5 + 4 * q^6 + 8 * q^8	$ 4 q - 4 q^{2} - 2 q^{3} + 6 q^{5} + 4 q^{6} + 8 q^{8} - 18 q^{10} + 16 q^{11} - 4 q^{12} - 8 q^{13} - 30 q^{15} - 16 q^{16} - 62 q^{17} + 12 q^{18} + 24 q^{20} - 16 q^{22} - 22 q^{23} + 6 q^{25} + 16 q^{26} - 2 q^{27} + 50 q^{30} - 24 q^{31} + 16 q^{32} - 30 q^{33} - 24 q^{36} + 134 q^{37} + 12 q^{38} - 12 q^{40} + 160 q^{41} + 8 q^{43} + 58 q^{45} + 44 q^{46} - 102 q^{47} + 8 q^{48} + 2 q^{50} - 48 q^{51} - 16 q^{52} - 98 q^{53} + 68 q^{55} + 38 q^{57} + 40 q^{58} - 40 q^{60} + 84 q^{61} + 24 q^{62} + 210 q^{65} + 60 q^{66} + 130 q^{67} + 124 q^{68} + 200 q^{71} + 24 q^{72} + 246 q^{73} - 40 q^{75} - 24 q^{76} + 124 q^{78} - 24 q^{80} + 136 q^{81} - 160 q^{82} - 80 q^{83} - 224 q^{85} - 16 q^{86} - 196 q^{87} + 32 q^{88} - 84 q^{90} - 44 q^{92} + 210 q^{93} + 80 q^{95} - 16 q^{96} - 216 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^3 + 6 * q^5 + 4 * q^6 + 8 * q^8 - 18 * q^10 + 16 * q^11 - 4 * q^12 - 8 * q^13 - 30 * q^15 - 16 * q^16 - 62 * q^17 + 12 * q^18 + 24 * q^20 - 16 * q^22 - 22 * q^23 + 6 * q^25 + 16 * q^26 - 2 * q^27 + 50 * q^30 - 24 * q^31 + 16 * q^32 - 30 * q^33 - 24 * q^36 + 134 * q^37 + 12 * q^38 - 12 * q^40 + 160 * q^41 + 8 * q^43 + 58 * q^45 + 44 * q^46 - 102 * q^47 + 8 * q^48 + 2 * q^50 - 48 * q^51 - 16 * q^52 - 98 * q^53 + 68 * q^55 + 38 * q^57 + 40 * q^58 - 40 * q^60 + 84 * q^61 + 24 * q^62 + 210 * q^65 + 60 * q^66 + 130 * q^67 + 124 * q^68 + 200 * q^71 + 24 * q^72 + 246 * q^73 - 40 * q^75 - 24 * q^76 + 124 * q^78 - 24 * q^80 + 136 * q^81 - 160 * q^82 - 80 * q^83 - 224 * q^85 - 16 * q^86 - 196 * q^87 + 32 * q^88 - 84 * q^90 - 44 * q^92 + 210 * q^93 + 80 * q^95 - 16 * q^96 - 216 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.15831	+	1.15831i	0.386104	+	0.386104i	0.873295	−	0.487191i	$-0.161979\pi$
$3$	1.15831	+	1.15831i	0.386104	+	0.386104i	−0.487191	+	0.873295i	$0.661979\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−1.81662	+	4.65831i	−0.363325	+	0.931662i
$5$	−1.81662	+	4.65831i	−0.363325	+	0.931662i
$6$	−2.31662			−0.386104
$7$		0			0
$7$		0			0
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		−	6.31662i		−	0.701847i
$10$	−2.84169	−	6.47494i	−0.284169	−	0.647494i
$11$	0.683375			0.0621250			0.0310625	−	0.999517i	$-0.490111\pi$
$11$	0.683375			0.0621250			0.0310625	+	0.999517i	$0.490111\pi$
$12$	2.31662	−	2.31662i	0.193052	−	0.193052i
$13$	−11.9499	−	11.9499i	−0.919221	−	0.919221i	0.0777517	−	0.996973i	$-0.475226\pi$
$13$	−11.9499	−	11.9499i	−0.919221	−	0.919221i	−0.996973	+	0.0777517i	$0.975226\pi$
$14$		0			0
$15$	−7.50000	+	3.29156i	−0.500000	+	0.219437i
$16$	−4.00000			−0.250000
$17$	−23.7916	+	23.7916i	−1.39950	+	1.39950i	−0.598030	+	0.801474i	$0.704050\pi$
$17$	−23.7916	+	23.7916i	−1.39950	+	1.39950i	−0.801474	+	0.598030i	$0.795950\pi$
$18$	6.31662	+	6.31662i	0.350924	+	0.350924i
$19$		−	9.63325i		−	0.507013i	−0.967334	−	0.253507i	$-0.918416\pi$
$19$		−	9.63325i		−	0.507013i	0.967334	−	0.253507i	$-0.0815839\pi$
$20$	9.31662	+	3.63325i	0.465831	+	0.181662i
$21$		0			0
$22$	−0.683375	+	0.683375i	−0.0310625	+	0.0310625i
$23$	−17.1082	−	17.1082i	−0.743834	−	0.743834i	0.229479	−	0.973314i	$-0.426298\pi$
$23$	−17.1082	−	17.1082i	−0.743834	−	0.743834i	−0.973314	+	0.229479i	$0.926298\pi$
$24$			4.63325i			0.193052i
$25$	−18.3997	−	16.9248i	−0.735990	−	0.676992i
$26$	23.8997			0.919221
$27$	17.7414	−	17.7414i	0.657090	−	0.657090i
$28$		0			0
$29$			16.5330i			0.570103i	0.958512	+	0.285052i	$0.0920108\pi$
$29$			16.5330i			0.570103i	−0.958512	+	0.285052i	$0.907989\pi$
$30$	4.20844	−	10.7916i	0.140281	−	0.359719i
$31$	23.8496			0.769343			0.384671	−	0.923054i	$-0.374315\pi$
$31$	23.8496			0.769343			0.384671	+	0.923054i	$0.374315\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	0.791562	+	0.791562i	0.0239867	+	0.0239867i
$34$		−	47.5831i		−	1.39950i
$35$		0			0
$36$	−12.6332			−0.350924
$37$	18.5752	−	18.5752i	0.502032	−	0.502032i	−0.410037	−	0.912069i	$-0.634484\pi$
$37$	18.5752	−	18.5752i	0.502032	−	0.502032i	0.912069	+	0.410037i	$0.134484\pi$
$38$	9.63325	+	9.63325i	0.253507	+	0.253507i
$39$		−	27.6834i		−	0.709830i
$40$	−12.9499	+	5.68338i	−0.323747	+	0.142084i
$41$	0.200503			0.00489031			0.00244515	−	0.999997i	$-0.499222\pi$
$41$	0.200503			0.00489031			0.00244515	+	0.999997i	$0.499222\pi$
$42$		0			0
$43$	−41.1161	−	41.1161i	−0.956189	−	0.956189i	0.0428909	−	0.999080i	$-0.486343\pi$
$43$	−41.1161	−	41.1161i	−0.956189	−	0.956189i	−0.999080	+	0.0428909i	$0.986343\pi$
$44$		−	1.36675i		−	0.0310625i
$45$	29.4248	+	11.4749i	0.653885	+	0.254999i
$46$	34.2164			0.743834
$47$	−33.7916	+	33.7916i	−0.718969	+	0.718969i	−0.968394	−	0.249425i	$-0.919758\pi$
$47$	−33.7916	+	33.7916i	−0.718969	+	0.718969i	0.249425	+	0.968394i	$0.419758\pi$
$48$	−4.63325	−	4.63325i	−0.0965260	−	0.0965260i
$49$		0			0
$50$	35.3246	−	1.47494i	0.706491	−	0.0294987i
$51$	−55.1161			−1.08071
$52$	−23.8997	+	23.8997i	−0.459611	+	0.459611i
$53$	−65.9578	−	65.9578i	−1.24449	−	1.24449i	−0.958120	−	0.286367i	$-0.907552\pi$
$53$	−65.9578	−	65.9578i	−1.24449	−	1.24449i	−0.286367	−	0.958120i	$-0.592448\pi$
$54$			35.4829i			0.657090i
$55$	−1.24144	+	3.18338i	−0.0225716	+	0.0578795i
$56$		0			0
$57$	11.1583	−	11.1583i	0.195760	−	0.195760i
$58$	−16.5330	−	16.5330i	−0.285052	−	0.285052i
$59$		−	23.1003i		−	0.391530i	−0.980651	−	0.195765i	$-0.937281\pi$
$59$		−	23.1003i		−	0.391530i	0.980651	−	0.195765i	$-0.0627189\pi$
$60$	6.58312	+	15.0000i	0.109719	+	0.250000i
$61$	−12.1662			−0.199447			−0.0997233	−	0.995015i	$-0.531796\pi$
$61$	−12.1662			−0.199447			−0.0997233	+	0.995015i	$0.531796\pi$
$62$	−23.8496	+	23.8496i	−0.384671	+	0.384671i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	77.3747	−	33.9578i	1.19038	−	0.522428i
$66$	−1.58312			−0.0239867
$67$	0.992064	−	0.992064i	0.0148069	−	0.0148069i	−0.699665	−	0.714471i	$-0.746667\pi$
$67$	0.992064	−	0.992064i	0.0148069	−	0.0148069i	0.714471	+	0.699665i	$0.246667\pi$
$68$	47.5831	+	47.5831i	0.699752	+	0.699752i
$69$		−	39.6332i		−	0.574395i
$70$		0			0
$71$	63.2665			0.891077			0.445539	−	0.895263i	$-0.353012\pi$
$71$	63.2665			0.891077			0.445539	+	0.895263i	$0.353012\pi$
$72$	12.6332	−	12.6332i	0.175462	−	0.175462i
$73$	33.3087	+	33.3087i	0.456283	+	0.456283i	0.897433	−	0.441150i	$-0.145429\pi$
$73$	33.3087	+	33.3087i	0.456283	+	0.456283i	−0.441150	+	0.897433i	$0.645429\pi$
$74$			37.1504i			0.502032i
$75$	−1.70844	−	40.9169i	−0.0227792	−	0.545558i
$76$	−19.2665			−0.253507
$77$		0			0
$78$	27.6834	+	27.6834i	0.354915	+	0.354915i
$79$		−	112.266i		−	1.42109i	−0.703649	−	0.710547i	$-0.748447\pi$
$79$		−	112.266i		−	1.42109i	0.703649	−	0.710547i	$-0.251553\pi$
$80$	7.26650	−	18.6332i	0.0908312	−	0.232916i
$81$	−15.7494			−0.194437
$82$	−0.200503	+	0.200503i	−0.00244515	+	0.00244515i
$83$	23.1161	+	23.1161i	0.278507	+	0.278507i	0.832513	−	0.554006i	$-0.186901\pi$
$83$	23.1161	+	23.1161i	0.278507	+	0.278507i	−0.554006	+	0.832513i	$0.686901\pi$
$84$		0			0
$85$	−67.6082	−	154.049i	−0.795390	−	1.81234i
$86$	82.2322			0.956189
$87$	−19.1504	+	19.1504i	−0.220119	+	0.220119i
$88$	1.36675	+	1.36675i	0.0155313	+	0.0155313i
$89$		−	79.8496i		−	0.897187i	−0.893736	−	0.448593i	$-0.851925\pi$
$89$		−	79.8496i		−	0.897187i	0.893736	−	0.448593i	$-0.148075\pi$
$90$	−40.8997	+	17.9499i	−0.454442	+	0.199443i
$91$		0			0
$92$	−34.2164	+	34.2164i	−0.371917	+	0.371917i
$93$	27.6253	+	27.6253i	0.297046	+	0.297046i
$94$		−	67.5831i		−	0.718969i
$95$	44.8747	+	17.5000i	0.472365	+	0.184211i
$96$	9.26650			0.0965260
$97$	−50.6834	+	50.6834i	−0.522509	+	0.522509i	−0.918328	−	0.395819i	$-0.870461\pi$
$97$	−50.6834	+	50.6834i	−0.522509	+	0.522509i	0.395819	+	0.918328i	$0.370461\pi$
$98$		0			0
$99$		−	4.31662i		−	0.0436023i
$100$	−33.8496	+	36.7995i	−0.338496	+	0.367995i
$101$	−55.0000			−0.544554			−0.272277	−	0.962219i	$-0.587777\pi$
$101$	−55.0000			−0.544554			−0.272277	+	0.962219i	$0.587777\pi$
$102$	55.1161	−	55.1161i	0.540354	−	0.540354i
$103$	0.158312	+	0.158312i	0.00153701	+	0.00153701i	0.707875	−	0.706338i	$-0.249654\pi$
$103$	0.158312	+	0.158312i	0.00153701	+	0.00153701i	−0.706338	+	0.707875i	$0.749654\pi$
$104$		−	47.7995i		−	0.459611i
$105$		0			0
$106$	131.916			1.24449
$107$	−95.1583	+	95.1583i	−0.889330	+	0.889330i	−0.994459	−	0.105129i	$-0.966475\pi$
$107$	−95.1583	+	95.1583i	−0.889330	+	0.889330i	0.105129	+	0.994459i	$0.466475\pi$
$108$	−35.4829	−	35.4829i	−0.328545	−	0.328545i
$109$			51.1161i			0.468955i	0.972122	+	0.234478i	$0.0753380\pi$
$109$			51.1161i			0.468955i	−0.972122	+	0.234478i	$0.924662\pi$
$110$	−1.94194	−	4.42481i	−0.0176540	−	0.0402256i
$111$	43.0317			0.387673
$112$		0			0
$113$	63.8496	+	63.8496i	0.565041	+	0.565041i	0.930735	−	0.365694i	$-0.119168\pi$
$113$	63.8496	+	63.8496i	0.565041	+	0.565041i	−0.365694	+	0.930735i	$0.619168\pi$
$114$			22.3166i			0.195760i
$115$	110.774	−	48.6161i	0.963256	−	0.422749i
$116$	33.0660			0.285052
$117$	−75.4829	+	75.4829i	−0.645153	+	0.645153i
$118$	23.1003	+	23.1003i	0.195765	+	0.195765i
$119$		0			0
$120$	−21.5831	−	8.41688i	−0.179859	−	0.0701406i
$121$	−120.533			−0.996140
$122$	12.1662	−	12.1662i	0.0997233	−	0.0997233i
$123$	0.232245	+	0.232245i	0.00188817	+	0.00188817i
$124$		−	47.6992i		−	0.384671i
$125$	112.266	−	54.9657i	0.898132	−	0.439726i
$126$		0			0
$127$	−108.082	+	108.082i	−0.851038	+	0.851038i	−0.990261	−	0.139223i	$-0.955540\pi$
$127$	−108.082	+	108.082i	−0.851038	+	0.851038i	0.139223	+	0.990261i	$0.455540\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	95.2506i		−	0.738377i
$130$	−43.4169	+	111.332i	−0.333976	+	0.856404i
$131$	58.8839			0.449495			0.224748	−	0.974417i	$-0.427844\pi$
$131$	58.8839			0.449495			0.224748	+	0.974417i	$0.427844\pi$
$132$	1.58312	−	1.58312i	0.0119934	−	0.0119934i
$133$		0			0
$134$			1.98413i			0.0148069i
$135$	50.4156	+	114.875i	0.373449	+	0.850924i
$136$	−95.1662			−0.699752
$137$	93.1742	−	93.1742i	0.680104	−	0.680104i	−0.279920	−	0.960023i	$-0.590308\pi$
$137$	93.1742	−	93.1742i	0.680104	−	0.680104i	0.960023	+	0.279920i	$0.0903079\pi$
$138$	39.6332	+	39.6332i	0.287197	+	0.287197i
$139$			68.2322i			0.490879i	0.969412	+	0.245440i	$0.0789323\pi$
$139$			68.2322i			0.490879i	−0.969412	+	0.245440i	$0.921068\pi$
$140$		0			0
$141$	−78.2824			−0.555194
$142$	−63.2665	+	63.2665i	−0.445539	+	0.445539i
$143$	−8.16625	−	8.16625i	−0.0571066	−	0.0571066i
$144$			25.2665i			0.175462i
$145$	−77.0159	−	30.0343i	−0.531144	−	0.207133i
$146$	−66.6174			−0.456283
$147$		0			0
$148$	−37.1504	−	37.1504i	−0.251016	−	0.251016i
$149$			87.4486i			0.586903i	0.955974	+	0.293452i	$0.0948040\pi$
$149$			87.4486i			0.586903i	−0.955974	+	0.293452i	$0.905196\pi$
$150$	42.6253	+	39.2084i	0.284169	+	0.261390i
$151$	−235.982			−1.56279			−0.781396	−	0.624035i	$-0.785492\pi$
$151$	−235.982			−1.56279			−0.781396	+	0.624035i	$0.785492\pi$
$152$	19.2665	−	19.2665i	0.126753	−	0.126753i
$153$	150.282	+	150.282i	0.982238	+	0.982238i
$154$		0			0
$155$	−43.3258	+	111.099i	−0.279521	+	0.716768i
$156$	−55.3668			−0.354915
$157$	−112.641	+	112.641i	−0.717460	+	0.717460i	−0.968084	−	0.250625i	$-0.919364\pi$
$157$	−112.641	+	112.641i	−0.717460	+	0.717460i	0.250625	+	0.968084i	$0.419364\pi$
$158$	112.266	+	112.266i	0.710547	+	0.710547i
$159$		−	152.799i		−	0.961003i
$160$	11.3668	+	25.8997i	0.0710422	+	0.161873i
$161$		0			0
$162$	15.7494	−	15.7494i	0.0972183	−	0.0972183i
$163$	176.523	+	176.523i	1.08296	+	1.08296i	0.996232	+	0.0867284i	$0.0276412\pi$
$163$	176.523	+	176.523i	1.08296	+	1.08296i	0.0867284	+	0.996232i	$0.472359\pi$
$164$		−	0.401005i		−	0.00244515i
$165$	−5.12531	+	2.24937i	−0.0310625	+	0.0136326i
$166$	−46.2322			−0.278507
$167$	−202.799	+	202.799i	−1.21437	+	1.21437i	−0.244793	+	0.969575i	$0.578720\pi$
$167$	−202.799	+	202.799i	−1.21437	+	1.21437i	−0.969575	+	0.244793i	$0.921280\pi$
$168$		0			0
$169$			116.599i			0.689935i
$170$	221.657	+	86.4407i	1.30387	+	0.508475i
$171$	−60.8496			−0.355846
$172$	−82.2322	+	82.2322i	−0.478094	+	0.478094i
$173$	−11.0739	−	11.0739i	−0.0640112	−	0.0640112i	0.674376	−	0.738388i	$-0.264412\pi$
$173$	−11.0739	−	11.0739i	−0.0640112	−	0.0640112i	−0.738388	+	0.674376i	$0.764412\pi$
$174$		−	38.3008i		−	0.220119i
$175$		0			0
$176$	−2.73350			−0.0155313
$177$	26.7573	−	26.7573i	0.151171	−	0.151171i
$178$	79.8496	+	79.8496i	0.448593	+	0.448593i
$179$			342.900i			1.91564i	0.287367	+	0.957821i	$0.407220\pi$
$179$			342.900i			1.91564i	−0.287367	+	0.957821i	$0.592780\pi$
$180$	22.9499	−	58.8496i	0.127499	−	0.326942i
$181$	−88.1320			−0.486917			−0.243459	−	0.969911i	$-0.578282\pi$
$181$	−88.1320			−0.486917			−0.243459	+	0.969911i	$0.578282\pi$
$182$		0			0
$183$	−14.0923	−	14.0923i	−0.0770072	−	0.0770072i
$184$		−	68.4327i		−	0.371917i
$185$	52.7849	+	120.273i	0.285324	+	0.650125i
$186$	−55.2506			−0.297046
$187$	−16.2586	+	16.2586i	−0.0869442	+	0.0869442i
$188$	67.5831	+	67.5831i	0.359485	+	0.359485i
$189$		0			0
$190$	−62.3747	+	27.3747i	−0.328288	+	0.144077i
$191$	−47.0844			−0.246515			−0.123258	−	0.992375i	$-0.539334\pi$
$191$	−47.0844			−0.246515			−0.123258	+	0.992375i	$0.539334\pi$
$192$	−9.26650	+	9.26650i	−0.0482630	+	0.0482630i
$193$	−72.3747	−	72.3747i	−0.374998	−	0.374998i	0.494296	−	0.869294i	$-0.335426\pi$
$193$	−72.3747	−	72.3747i	−0.374998	−	0.374998i	−0.869294	+	0.494296i	$0.835426\pi$
$194$		−	101.367i		−	0.522509i
$195$	128.958	+	50.2903i	0.661322	+	0.257899i
$196$		0			0
$197$	163.148	−	163.148i	0.828162	−	0.828162i	−0.159101	−	0.987262i	$-0.550859\pi$
$197$	163.148	−	163.148i	0.828162	−	0.828162i	0.987262	+	0.159101i	$0.0508594\pi$
$198$	4.31662	+	4.31662i	0.0218011	+	0.0218011i
$199$		−	340.731i		−	1.71222i	−0.516797	−	0.856108i	$-0.672876\pi$
$199$		−	340.731i		−	1.71222i	0.516797	−	0.856108i	$-0.327124\pi$
$200$	−2.94987	−	70.6491i	−0.0147494	−	0.353246i
$201$	2.29824			0.0114340
$202$	55.0000	−	55.0000i	0.272277	−	0.272277i
$203$		0			0
$204$			110.232i			0.540354i
$205$	−0.364238	+	0.934003i	−0.00177677	+	0.00455611i
$206$	−0.316625			−0.00153701
$207$	−108.066	+	108.066i	−0.522058	+	0.522058i
$208$	47.7995	+	47.7995i	0.229805	+	0.229805i
$209$		−	6.58312i		−	0.0314982i
$210$		0			0
$211$	113.799			0.539334			0.269667	−	0.962954i	$-0.413086\pi$
$211$	113.799			0.539334			0.269667	+	0.962954i	$0.413086\pi$
$212$	−131.916	+	131.916i	−0.622243	+	0.622243i
$213$	73.2824	+	73.2824i	0.344049	+	0.344049i
$214$		−	190.317i		−	0.889330i
$215$	266.224	−	116.839i	1.23825	−	0.543438i
$216$	70.9657			0.328545
$217$		0			0
$218$	−51.1161	−	51.1161i	−0.234478	−	0.234478i
$219$			77.1637i			0.352346i
$220$	6.36675	+	2.48287i	0.0289398	+	0.0112858i
$221$	568.612			2.57291
$222$	−43.0317	+	43.0317i	−0.193837	+	0.193837i
$223$	−158.916	−	158.916i	−0.712626	−	0.712626i	0.254458	−	0.967084i	$-0.418103\pi$
$223$	−158.916	−	158.916i	−0.712626	−	0.712626i	−0.967084	+	0.254458i	$0.918103\pi$
$224$		0			0
$225$	−106.908	+	116.224i	−0.475145	+	0.516552i
$226$	−127.699			−0.565041
$227$	−201.858	+	201.858i	−0.889240	+	0.889240i	−0.994450	−	0.105210i	$-0.966449\pi$
$227$	−201.858	+	201.858i	−0.889240	+	0.889240i	0.105210	+	0.994450i	$0.466449\pi$
$228$	−22.3166	−	22.3166i	−0.0978799	−	0.0978799i
$229$			313.348i			1.36833i	0.729326	+	0.684167i	$0.239834\pi$
$229$			313.348i			1.36833i	−0.729326	+	0.684167i	$0.760166\pi$
$230$	−62.1583	+	159.391i	−0.270254	+	0.693002i
$231$		0			0
$232$	−33.0660	+	33.0660i	−0.142526	+	0.142526i
$233$	35.7757	+	35.7757i	0.153544	+	0.153544i	0.779699	−	0.626155i	$-0.215372\pi$
$233$	35.7757	+	35.7757i	0.153544	+	0.153544i	−0.626155	+	0.779699i	$0.715372\pi$
$234$		−	150.966i		−	0.645153i
$235$	−96.0251	−	218.798i	−0.408617	−	0.931056i
$236$	−46.2005			−0.195765
$237$	130.040	−	130.040i	0.548691	−	0.548691i
$238$		0			0
$239$		−	195.330i		−	0.817280i	−0.912696	−	0.408640i	$-0.866003\pi$
$239$		−	195.330i		−	0.817280i	0.912696	−	0.408640i	$-0.133997\pi$
$240$	30.0000	−	13.1662i	0.125000	−	0.0548594i
$241$	92.9315			0.385608			0.192804	−	0.981237i	$-0.438242\pi$
$241$	92.9315			0.385608			0.192804	+	0.981237i	$0.438242\pi$
$242$	120.533	−	120.533i	0.498070	−	0.498070i
$243$	−177.916	−	177.916i	−0.732163	−	0.732163i
$244$			24.3325i			0.0997233i
$245$		0			0
$246$	−0.464489			−0.00188817
$247$	−115.116	+	115.116i	−0.466057	+	0.466057i
$248$	47.6992	+	47.6992i	0.192336	+	0.192336i
$249$			53.5514i			0.215066i
$250$	−57.3008	+	167.232i	−0.229203	+	0.668929i
$251$	−332.665			−1.32536			−0.662679	−	0.748903i	$-0.730581\pi$
$251$	−332.665			−1.32536			−0.662679	+	0.748903i	$0.730581\pi$
$252$		0			0
$253$	−11.6913	−	11.6913i	−0.0462107	−	0.0462107i
$254$		−	216.164i		−	0.851038i
$255$	100.125	−	256.748i	0.392648	−	1.00686i
$256$	16.0000			0.0625000
$257$	72.3906	−	72.3906i	0.281675	−	0.281675i	−0.552102	−	0.833777i	$-0.686174\pi$
$257$	72.3906	−	72.3906i	0.281675	−	0.281675i	0.833777	+	0.552102i	$0.186174\pi$
$258$	95.2506	+	95.2506i	0.369188	+	0.369188i
$259$		0			0
$260$	−67.9156	−	154.749i	−0.261214	−	0.595190i
$261$	104.433			0.400125
$262$	−58.8839	+	58.8839i	−0.224748	+	0.224748i
$263$	141.391	+	141.391i	0.537607	+	0.537607i	0.922825	−	0.385219i	$-0.125874\pi$
$263$	141.391	+	141.391i	0.537607	+	0.537607i	−0.385219	+	0.922825i	$0.625874\pi$
$264$			3.16625i			0.0119934i
$265$	427.073	−	187.431i	1.61160	−	0.707289i
$266$		0			0
$267$	92.4908	−	92.4908i	0.346408	−	0.346408i
$268$	−1.98413	−	1.98413i	−0.00740347	−	0.00740347i
$269$		−	229.248i		−	0.852223i	−0.904671	−	0.426112i	$-0.859883\pi$
$269$		−	229.248i		−	0.852223i	0.904671	−	0.426112i	$-0.140117\pi$
$270$	−165.290	−	64.4591i	−0.612186	−	0.238737i
$271$	56.1821			0.207314			0.103657	−	0.994613i	$-0.466946\pi$
$271$	56.1821			0.207314			0.103657	+	0.994613i	$0.466946\pi$
$272$	95.1662	−	95.1662i	0.349876	−	0.349876i
$273$		0			0
$274$			186.348i			0.680104i
$275$	−12.5739	−	11.5660i	−0.0457234	−	0.0420582i
$276$	−79.2665			−0.287197
$277$	−60.0079	+	60.0079i	−0.216635	+	0.216635i	−0.807079	−	0.590444i	$-0.798953\pi$
$277$	−60.0079	+	60.0079i	−0.216635	+	0.216635i	0.590444	+	0.807079i	$0.298953\pi$
$278$	−68.2322	−	68.2322i	−0.245440	−	0.245440i
$279$		−	150.649i		−	0.539961i
$280$		0			0
$281$	136.201			0.484699			0.242350	−	0.970189i	$-0.422082\pi$
$281$	136.201			0.484699			0.242350	+	0.970189i	$0.422082\pi$
$282$	78.2824	−	78.2824i	0.277597	−	0.277597i
$283$	222.441	+	222.441i	0.786009	+	0.786009i	0.980837	−	0.194828i	$-0.0624149\pi$
$283$	222.441	+	222.441i	0.786009	+	0.786009i	−0.194828	+	0.980837i	$0.562415\pi$
$284$		−	126.533i		−	0.445539i
$285$	31.7084	+	72.2494i	0.111258	+	0.253507i
$286$	16.3325			0.0571066
$287$		0			0
$288$	−25.2665	−	25.2665i	−0.0877309	−	0.0877309i
$289$		−	843.077i		−	2.91722i
$290$	107.050	−	46.9816i	0.369138	−	0.162006i
$291$	−117.414			−0.403486
$292$	66.6174	−	66.6174i	0.228142	−	0.228142i
$293$	−184.699	−	184.699i	−0.630373	−	0.630373i	0.317789	−	0.948162i	$-0.397060\pi$
$293$	−184.699	−	184.699i	−0.630373	−	0.630373i	−0.948162	+	0.317789i	$0.897060\pi$
$294$		0			0
$295$	107.608	+	41.9645i	0.364774	+	0.142253i
$296$	74.3008			0.251016
$297$	12.1241	−	12.1241i	0.0408217	−	0.0408217i
$298$	−87.4486	−	87.4486i	−0.293452	−	0.293452i
$299$			408.881i			1.36750i
$300$	−81.8338	+	3.41688i	−0.272779	+	0.0113896i
$301$		0			0
$302$	235.982	−	235.982i	0.781396	−	0.781396i
$303$	−63.7072	−	63.7072i	−0.210255	−	0.210255i
$304$			38.5330i			0.126753i
$305$	22.1015	−	56.6742i	0.0724640	−	0.185817i
$306$	−300.565			−0.982238
$307$	−370.647	+	370.647i	−1.20732	+	1.20732i	−0.235426	+	0.971892i	$0.575648\pi$
$307$	−370.647	+	370.647i	−1.20732	+	1.20732i	−0.971892	+	0.235426i	$0.924352\pi$
$308$		0			0
$309$			0.366750i			0.00118689i
$310$	−67.7732	−	154.425i	−0.218623	−	0.498145i
$311$	−439.079			−1.41183			−0.705915	−	0.708296i	$-0.749464\pi$
$311$	−439.079			−1.41183			−0.705915	+	0.708296i	$0.749464\pi$
$312$	55.3668	−	55.3668i	0.177458	−	0.177458i
$313$	147.122	+	147.122i	0.470037	+	0.470037i	0.901926	−	0.431890i	$-0.142153\pi$
$313$	147.122	+	147.122i	0.470037	+	0.470037i	−0.431890	+	0.901926i	$0.642153\pi$
$314$		−	225.282i		−	0.717460i
$315$		0			0
$316$	−224.533			−0.710547
$317$	291.673	−	291.673i	0.920104	−	0.920104i	−0.0769324	−	0.997036i	$-0.524513\pi$
$317$	291.673	−	291.673i	0.920104	−	0.920104i	0.997036	+	0.0769324i	$0.0245126\pi$
$318$	152.799	+	152.799i	0.480502	+	0.480502i
$319$			11.2982i			0.0354177i
$320$	−37.2665	−	14.5330i	−0.116458	−	0.0454156i
$321$	−220.446			−0.686748
$322$		0			0
$323$	229.190	+	229.190i	0.709567	+	0.709567i
$324$			31.4987i			0.0972183i
$325$	17.6253	+	422.124i	0.0542317	+	1.29884i
$326$	−353.045			−1.08296
$327$	−59.2084	+	59.2084i	−0.181066	+	0.181066i
$328$	0.401005	+	0.401005i	0.00122258	+	0.00122258i
$329$		0			0
$330$	2.87594	−	7.37469i	0.00871498	−	0.0223475i
$331$	−373.380			−1.12804			−0.564018	−	0.825762i	$-0.690745\pi$
$331$	−373.380			−1.12804			−0.564018	+	0.825762i	$0.690745\pi$
$332$	46.2322	−	46.2322i	0.139254	−	0.139254i
$333$	−117.332	−	117.332i	−0.352350	−	0.352350i
$334$		−	405.599i		−	1.21437i
$335$	2.81914	+	6.42356i	0.00841534	+	0.0191748i
$336$		0			0
$337$	259.016	−	259.016i	0.768593	−	0.768593i	−0.209266	−	0.977859i	$-0.567107\pi$
$337$	259.016	−	259.016i	0.768593	−	0.768593i	0.977859	+	0.209266i	$0.0671074\pi$
$338$	−116.599	−	116.599i	−0.344967	−	0.344967i
$339$			147.916i			0.436329i
$340$	−308.098	+	135.216i	−0.906170	+	0.397695i
$341$	16.2982			0.0477954
$342$	60.8496	−	60.8496i	0.177923	−	0.177923i
$343$		0			0
$344$		−	164.464i		−	0.478094i
$345$	184.624	+	71.9987i	0.535142	+	0.208692i
$346$	22.1479			0.0640112
$347$	234.222	−	234.222i	0.674991	−	0.674991i	−0.283872	−	0.958862i	$-0.591619\pi$
$347$	234.222	−	234.222i	0.674991	−	0.674991i	0.958862	+	0.283872i	$0.0916189\pi$
$348$	38.3008	+	38.3008i	0.110060	+	0.110060i
$349$		−	383.298i		−	1.09828i	−0.835732	−	0.549138i	$-0.814956\pi$
$349$		−	383.298i		−	1.09828i	0.835732	−	0.549138i	$-0.185044\pi$
$350$		0			0
$351$	−424.016			−1.20802
$352$	2.73350	−	2.73350i	0.00776563	−	0.00776563i
$353$	−394.375	−	394.375i	−1.11721	−	1.11721i	−0.992149	−	0.125059i	$-0.960088\pi$
$353$	−394.375	−	394.375i	−1.11721	−	1.11721i	−0.125059	−	0.992149i	$-0.539912\pi$
$354$			53.5146i			0.151171i
$355$	−114.931	+	294.715i	−0.323751	+	0.830183i
$356$	−159.699			−0.448593
$357$		0			0
$358$	−342.900	−	342.900i	−0.957821	−	0.957821i
$359$		−	220.166i		−	0.613276i	−0.951826	−	0.306638i	$-0.900796\pi$
$359$		−	220.166i		−	0.613276i	0.951826	−	0.306638i	$-0.0992042\pi$
$360$	35.8997	+	81.7995i	0.0997215	+	0.227221i
$361$	268.201			0.742938
$362$	88.1320	−	88.1320i	0.243459	−	0.243459i
$363$	−139.615	−	139.615i	−0.384614	−	0.384614i
$364$		0			0
$365$	−215.672	+	94.6529i	−0.590881	+	0.259323i
$366$	28.1846			0.0770072
$367$	346.924	−	346.924i	0.945296	−	0.945296i	−0.0532836	−	0.998579i	$-0.516969\pi$
$367$	346.924	−	346.924i	0.945296	−	0.945296i	0.998579	+	0.0532836i	$0.0169687\pi$
$368$	68.4327	+	68.4327i	0.185959	+	0.185959i
$369$		−	1.26650i		−	0.00343225i
$370$	−173.058	−	67.4883i	−0.467724	−	0.182401i
$371$		0			0
$372$	55.2506	−	55.2506i	0.148523	−	0.148523i
$373$	30.9946	+	30.9946i	0.0830954	+	0.0830954i	0.747433	−	0.664337i	$-0.231286\pi$
$373$	30.9946	+	30.9946i	0.0830954	+	0.0830954i	−0.664337	+	0.747433i	$0.731286\pi$
$374$		−	32.5171i		−	0.0869442i
$375$	193.707	+	66.3722i	0.516552	+	0.176992i
$376$	−135.166			−0.359485
$377$	197.567	−	197.567i	0.524051	−	0.524051i
$378$		0			0
$379$			393.135i			1.03729i	0.854988	+	0.518647i	$0.173564\pi$
$379$			393.135i			1.03729i	−0.854988	+	0.518647i	$0.826436\pi$
$380$	35.0000	−	89.7494i	0.0921053	−	0.236183i
$381$	−250.385			−0.657179
$382$	47.0844	−	47.0844i	0.123258	−	0.123258i
$383$	84.3747	+	84.3747i	0.220299	+	0.220299i	0.808625	−	0.588325i	$-0.200212\pi$
$383$	84.3747	+	84.3747i	0.220299	+	0.220299i	−0.588325	+	0.808625i	$0.700212\pi$
$384$		−	18.5330i		−	0.0482630i
$385$		0			0
$386$	144.749			0.374998
$387$	−259.715	+	259.715i	−0.671098	+	0.671098i
$388$	101.367	+	101.367i	0.261255	+	0.261255i
$389$		−	426.710i		−	1.09694i	−0.836170	−	0.548471i	$-0.815210\pi$
$389$		−	426.710i		−	1.09694i	0.836170	−	0.548471i	$-0.184790\pi$
$390$	−179.248	+	78.6675i	−0.459611	+	0.201712i
$391$	814.061			2.08200
$392$		0			0
$393$	68.2059	+	68.2059i	0.173552	+	0.173552i
$394$			326.296i			0.828162i
$395$	522.972	+	203.946i	1.32398	+	0.516319i
$396$	−8.63325			−0.0218011
$397$	−77.6412	+	77.6412i	−0.195570	+	0.195570i	−0.798098	−	0.602528i	$-0.794160\pi$
$397$	−77.6412	+	77.6412i	−0.195570	+	0.195570i	0.602528	+	0.798098i	$0.294160\pi$
$398$	340.731	+	340.731i	0.856108	+	0.856108i
$399$		0			0
$400$	73.5990	+	67.6992i	0.183997	+	0.169248i
$401$	78.8997			0.196757			0.0983787	−	0.995149i	$-0.468634\pi$
$401$	78.8997			0.196757			0.0983787	+	0.995149i	$0.468634\pi$
$402$	−2.29824	+	2.29824i	−0.00571702	+	0.00571702i
$403$	−285.000	−	285.000i	−0.707196	−	0.707196i
$404$			110.000i			0.272277i
$405$	28.6107	−	73.3655i	0.0706437	−	0.181149i
$406$		0			0
$407$	12.6938	−	12.6938i	0.0311888	−	0.0311888i
$408$	−110.232	−	110.232i	−0.270177	−	0.270177i
$409$			393.544i			0.962210i	0.876663	+	0.481105i	$0.159764\pi$
$409$			393.544i			0.962210i	−0.876663	+	0.481105i	$0.840236\pi$
$410$	−0.569766	−	1.29824i	−0.00138967	−	0.00316644i
$411$	215.850			0.525182
$412$	0.316625	−	0.316625i	0.000768507	−	0.000768507i
$413$		0			0
$414$		−	216.132i		−	0.522058i
$415$	−149.675	+	65.6888i	−0.360664	+	0.158286i
$416$	−95.5990			−0.229805
$417$	−79.0343	+	79.0343i	−0.189531	+	0.189531i
$418$	6.58312	+	6.58312i	0.0157491	+	0.0157491i
$419$			165.330i			0.394582i	0.980345	+	0.197291i	$0.0632144\pi$
$419$			165.330i			0.394582i	−0.980345	+	0.197291i	$0.936786\pi$
$420$		0			0
$421$	163.631			0.388672			0.194336	−	0.980935i	$-0.437745\pi$
$421$	163.631			0.388672			0.194336	+	0.980935i	$0.437745\pi$
$422$	−113.799	+	113.799i	−0.269667	+	0.269667i
$423$	213.449	+	213.449i	0.504607	+	0.504607i
$424$		−	263.831i		−	0.622243i
$425$	840.426	−	35.0911i	1.97747	−	0.0825672i
$426$	−146.565			−0.344049
$427$		0			0
$428$	190.317	+	190.317i	0.444665	+	0.444665i
$429$		−	18.9181i		−	0.0440982i
$430$	−149.385	+	383.063i	−0.347407	+	0.890845i
$431$	419.744			0.973885			0.486942	−	0.873434i	$-0.338112\pi$
$431$	419.744			0.973885			0.486942	+	0.873434i	$0.338112\pi$
$432$	−70.9657	+	70.9657i	−0.164273	+	0.164273i
$433$	−355.950	−	355.950i	−0.822055	−	0.822055i	0.164347	−	0.986403i	$-0.447448\pi$
$433$	−355.950	−	355.950i	−0.822055	−	0.822055i	−0.986403	+	0.164347i	$0.947448\pi$
$434$		0			0
$435$	−54.4194	−	123.997i	−0.125102	−	0.285052i
$436$	102.232			0.234478
$437$	−164.807	+	164.807i	−0.377134	+	0.377134i
$438$	−77.1637	−	77.1637i	−0.176173	−	0.176173i
$439$		−	187.765i		−	0.427711i	−0.976865	−	0.213856i	$-0.931398\pi$
$439$		−	187.765i		−	0.427711i	0.976865	−	0.213856i	$-0.0686022\pi$
$440$	−8.84962	+	3.88388i	−0.0201128	+	0.00882699i
$441$		0			0
$442$	−568.612	+	568.612i	−1.28645	+	1.28645i
$443$	423.071	+	423.071i	0.955014	+	0.955014i	0.999031	−	0.0440163i	$-0.0140154\pi$
$443$	423.071	+	423.071i	0.955014	+	0.955014i	−0.0440163	+	0.999031i	$0.514015\pi$
$444$		−	86.0635i		−	0.193837i
$445$	371.964	+	145.057i	0.835875	+	0.325970i
$446$	317.831			0.712626
$447$	−101.293	+	101.293i	−0.226606	+	0.226606i
$448$		0			0
$449$			93.8630i			0.209049i	0.994522	+	0.104524i	$0.0333321\pi$
$449$			93.8630i			0.209049i	−0.994522	+	0.104524i	$0.966668\pi$
$450$	−9.31662	−	223.132i	−0.0207036	−	0.495849i
$451$	0.137018			0.000303810
$452$	127.699	−	127.699i	0.282520	−	0.282520i
$453$	−273.340	−	273.340i	−0.603401	−	0.603401i
$454$		−	403.715i		−	0.889240i
$455$		0			0
$456$	44.6332			0.0978799
$457$	149.942	−	149.942i	0.328101	−	0.328101i	−0.523763	−	0.851864i	$-0.675472\pi$
$457$	149.942	−	149.942i	0.328101	−	0.328101i	0.851864	+	0.523763i	$0.175472\pi$
$458$	−313.348	−	313.348i	−0.684167	−	0.684167i
$459$			844.193i			1.83920i
$460$	−97.2322	−	221.549i	−0.211374	−	0.481628i
$461$	350.396			0.760078			0.380039	−	0.924970i	$-0.375911\pi$
$461$	350.396			0.760078			0.380039	+	0.924970i	$0.375911\pi$
$462$		0			0
$463$	−327.380	−	327.380i	−0.707084	−	0.707084i	0.258837	−	0.965921i	$-0.416661\pi$
$463$	−327.380	−	327.380i	−0.707084	−	0.707084i	−0.965921	+	0.258837i	$0.916661\pi$
$464$		−	66.1320i		−	0.142526i
$465$	−178.872	+	78.5025i	−0.384671	+	0.168823i
$466$	−71.5514			−0.153544
$467$	384.689	−	384.689i	0.823745	−	0.823745i	−0.162898	−	0.986643i	$-0.552084\pi$
$467$	384.689	−	384.689i	0.823745	−	0.823745i	0.986643	+	0.162898i	$0.0520842\pi$
$468$	150.966	+	150.966i	0.322576	+	0.322576i
$469$		0			0
$470$	314.823	+	122.773i	0.669837	+	0.261220i
$471$	−260.947			−0.554028
$472$	46.2005	−	46.2005i	0.0978824	−	0.0978824i
$473$	−28.0977	−	28.0977i	−0.0594033	−	0.0594033i
$474$			260.079i			0.548691i
$475$	−163.041	+	177.249i	−0.343244	+	0.373157i
$476$		0			0
$477$	−416.631	+	416.631i	−0.873440	+	0.873440i
$478$	195.330	+	195.330i	0.408640	+	0.408640i
$479$			67.6332i			0.141197i	0.997505	+	0.0705984i	$0.0224909\pi$
$479$			67.6332i			0.141197i	−0.997505	+	0.0705984i	$0.977509\pi$
$480$	−16.8338	+	43.1662i	−0.0350703	+	0.0899297i
$481$	−443.942			−0.922957
$482$	−92.9315	+	92.9315i	−0.192804	+	0.192804i
$483$		0			0
$484$			241.066i			0.498070i
$485$	−144.026	−	328.172i	−0.296961	−	0.676643i
$486$	355.831			0.732163
$487$	−527.172	+	527.172i	−1.08249	+	1.08249i	−0.0862111	+	0.996277i	$0.527476\pi$
$487$	−527.172	+	527.172i	−1.08249	+	1.08249i	−0.996277	+	0.0862111i	$0.972524\pi$
$488$	−24.3325	−	24.3325i	−0.0498617	−	0.0498617i
$489$			408.937i			0.836271i
$490$		0			0
$491$	199.061			0.405419			0.202710	−	0.979239i	$-0.435025\pi$
$491$	199.061			0.405419			0.202710	+	0.979239i	$0.435025\pi$
$492$	0.464489	−	0.464489i	0.000944084	−	0.000944084i
$493$	−393.346	−	393.346i	−0.797862	−	0.797862i
$494$		−	230.232i		−	0.466057i
$495$	20.1082	+	7.84169i	0.0406226	+	0.0158418i
$496$	−95.3985			−0.192336
$497$		0			0
$498$	−53.5514	−	53.5514i	−0.107533	−	0.107533i
$499$			544.799i			1.09178i	0.837856	+	0.545891i	$0.183809\pi$
$499$			544.799i			1.09178i	−0.837856	+	0.545891i	$0.816191\pi$
$500$	−109.931	−	224.533i	−0.219863	−	0.449066i
$501$	−469.810			−0.937745
$502$	332.665	−	332.665i	0.662679	−	0.662679i
$503$	−38.0869	−	38.0869i	−0.0757195	−	0.0757195i	0.668233	−	0.743952i	$-0.267051\pi$
$503$	−38.0869	−	38.0869i	−0.0757195	−	0.0757195i	−0.743952	+	0.668233i	$0.767051\pi$
$504$		0			0
$505$	99.9144	−	256.207i	0.197850	−	0.507341i
$506$	23.3826			0.0462107
$507$	−135.058	+	135.058i	−0.266387	+	0.266387i
$508$	216.164	+	216.164i	0.425519	+	0.425519i
$509$		−	173.143i		−	0.340163i	−0.985430	−	0.170081i	$-0.945597\pi$
$509$		−	173.143i		−	0.340163i	0.985430	−	0.170081i	$-0.0544031\pi$
$510$	156.623	+	356.873i	0.307104	+	0.699752i
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−170.908	−	170.908i	−0.333153	−	0.333153i
$514$			144.781i			0.281675i
$515$	−1.02506	+	0.449874i	−0.00199041	+	0.000873542i
$516$	−190.501			−0.369188
$517$	−23.0923	+	23.0923i	−0.0446660	+	0.0446660i
$518$		0			0
$519$		−	25.6541i		−	0.0494300i
$520$	222.665	+	86.8338i	0.428202	+	0.166988i
$521$	242.694			0.465824			0.232912	−	0.972498i	$-0.425175\pi$
$521$	242.694			0.465824			0.232912	+	0.972498i	$0.425175\pi$
$522$	−104.433	+	104.433i	−0.200063	+	0.200063i
$523$	−563.657	−	563.657i	−1.07774	−	1.07774i	−0.996712	−	0.0810262i	$-0.974180\pi$
$523$	−563.657	−	563.657i	−1.07774	−	1.07774i	−0.0810262	−	0.996712i	$-0.525820\pi$
$524$		−	117.768i		−	0.224748i
$525$		0			0
$526$	−282.781			−0.537607
$527$	−567.420	+	567.420i	−1.07670	+	1.07670i
$528$	−3.16625	−	3.16625i	−0.00599668	−	0.00599668i
$529$			56.3801i			0.106579i
$530$	−239.641	+	614.504i	−0.452153	+	1.15944i
$531$	−145.916			−0.274794
$532$		0			0
$533$	−2.39598	−	2.39598i	−0.00449527	−	0.00449527i
$534$			184.982i			0.346408i
$535$	−270.410	−	616.144i	−0.505440	−	1.15167i
$536$	3.96826			0.00740347
$537$	−397.185	+	397.185i	−0.739637	+	0.739637i
$538$	229.248	+	229.248i	0.426112	+	0.426112i
$539$		0			0
$540$	229.749	−	100.831i	0.425462	−	0.186725i
$541$	549.623			1.01594			0.507970	−	0.861375i	$-0.330396\pi$
$541$	549.623			1.01594			0.507970	+	0.861375i	$0.330396\pi$
$542$	−56.1821	+	56.1821i	−0.103657	+	0.103657i
$543$	−102.084	−	102.084i	−0.188001	−	0.188001i
$544$			190.332i			0.349876i
$545$	−238.115	−	92.8588i	−0.436908	−	0.170383i
$546$		0			0
$547$	469.765	−	469.765i	0.858803	−	0.858803i	−0.132394	−	0.991197i	$-0.542266\pi$
$547$	469.765	−	469.765i	0.858803	−	0.858803i	0.991197	+	0.132394i	$0.0422665\pi$
$548$	−186.348	−	186.348i	−0.340052	−	0.340052i
$549$			76.8496i			0.139981i
$550$	24.1399	−	1.00794i	0.0438908	−	0.00183261i
$551$	159.266			0.289050
$552$	79.2665	−	79.2665i	0.143599	−	0.143599i
$553$		0			0
$554$		−	120.016i		−	0.216635i
$555$	−78.1725	+	200.455i	−0.140851	+	0.361181i
$556$	136.464			0.245440
$557$	−269.855	+	269.855i	−0.484479	+	0.484479i	−0.906559	−	0.422079i	$-0.861300\pi$
$557$	−269.855	+	269.855i	−0.484479	+	0.484479i	0.422079	+	0.906559i	$0.361300\pi$
$558$	150.649	+	150.649i	0.269981	+	0.269981i
$559$			982.665i			1.75790i
$560$		0			0
$561$	−37.6650			−0.0671390
$562$	−136.201	+	136.201i	−0.242350	+	0.242350i
$563$	−128.974	−	128.974i	−0.229083	−	0.229083i	0.583227	−	0.812310i	$-0.301790\pi$
$563$	−128.974	−	128.974i	−0.229083	−	0.229083i	−0.812310	+	0.583227i	$0.801790\pi$
$564$			156.565i			0.277597i
$565$	−413.422	+	181.441i	−0.731721	+	0.321134i
$566$	−444.881			−0.786009
$567$		0			0
$568$	126.533	+	126.533i	0.222769	+	0.222769i
$569$			747.549i			1.31379i	0.753980	+	0.656897i	$0.228131\pi$
$569$			747.549i			1.31379i	−0.753980	+	0.656897i	$0.771869\pi$
$570$	−103.958	−	40.5409i	−0.182382	−	0.0711244i
$571$	184.145			0.322496			0.161248	−	0.986914i	$-0.448448\pi$
$571$	184.145			0.322496			0.161248	+	0.986914i	$0.448448\pi$
$572$	−16.3325	+	16.3325i	−0.0285533	+	0.0285533i
$573$	−54.5384	−	54.5384i	−0.0951805	−	0.0951805i
$574$		0			0
$575$	25.2335	+	604.339i	0.0438843	+	1.05102i
$576$	50.5330			0.0877309
$577$	701.222	−	701.222i	1.21529	−	1.21529i	0.246026	−	0.969263i	$-0.420875\pi$
$577$	701.222	−	701.222i	1.21529	−	1.21529i	0.969263	−	0.246026i	$-0.0791248\pi$
$578$	843.077	+	843.077i	1.45861	+	1.45861i
$579$		−	167.665i		−	0.289577i
$580$	−60.0685	+	154.032i	−0.103566	+	0.265572i
$581$		0			0
$582$	117.414	−	117.414i	0.201743	−	0.201743i
$583$	−45.0739	−	45.0739i	−0.0773138	−	0.0773138i
$584$			133.235i			0.228142i
$585$	−214.499	−	488.747i	−0.366665	−	0.835465i
$586$	369.398			0.630373
$587$	−103.786	+	103.786i	−0.176808	+	0.176808i	−0.789963	−	0.613155i	$-0.789900\pi$
$587$	−103.786	+	103.786i	−0.176808	+	0.176808i	0.613155	+	0.789963i	$0.289900\pi$
$588$		0			0
$589$		−	229.749i		−	0.390067i
$590$	−149.573	+	65.6437i	−0.253513	+	0.111261i
$591$	377.952			0.639513
$592$	−74.3008	+	74.3008i	−0.125508	+	0.125508i
$593$	65.8392	+	65.8392i	0.111027	+	0.111027i	0.760438	−	0.649411i	$-0.224984\pi$
$593$	65.8392	+	65.8392i	0.111027	+	0.111027i	−0.649411	+	0.760438i	$0.724984\pi$
$594$			24.2481i			0.0408217i
$595$		0			0
$596$	174.897			0.293452
$597$	394.673	−	394.673i	0.661094	−	0.661094i
$598$	−408.881	−	408.881i	−0.683748	−	0.683748i
$599$		−	542.626i		−	0.905886i	−0.891539	−	0.452943i	$-0.850374\pi$
$599$		−	542.626i		−	0.905886i	0.891539	−	0.452943i	$-0.149626\pi$
$600$	78.4169	−	85.2506i	0.130695	−	0.142084i
$601$	422.829			0.703542			0.351771	−	0.936086i	$-0.385580\pi$
$601$	422.829			0.703542			0.351771	+	0.936086i	$0.385580\pi$
$602$		0			0
$603$	−6.26650	−	6.26650i	−0.0103922	−	0.0103922i
$604$			471.963i			0.781396i
$605$	218.963	−	561.480i	0.361923	−	0.928067i
$606$	127.414			0.210255
$607$	−145.359	+	145.359i	−0.239471	+	0.239471i	−0.816631	−	0.577160i	$-0.804161\pi$
$607$	−145.359	+	145.359i	−0.239471	+	0.239471i	0.577160	+	0.816631i	$0.304161\pi$
$608$	−38.5330	−	38.5330i	−0.0633766	−	0.0633766i
$609$		0			0
$610$	34.5727	+	78.7757i	0.0566765	+	0.129140i
$611$	807.610			1.32178
$612$	300.565	−	300.565i	0.491119	−	0.491119i
$613$	177.589	+	177.589i	0.289704	+	0.289704i	0.836963	−	0.547259i	$-0.184329\pi$
$613$	177.589	+	177.589i	0.289704	+	0.289704i	−0.547259	+	0.836963i	$0.684329\pi$
$614$		−	741.293i		−	1.20732i
$615$	−1.50377	+	0.659966i	−0.00244515	+	0.00107312i
$616$		0			0
$617$	206.947	−	206.947i	0.335409	−	0.335409i	−0.519227	−	0.854636i	$-0.673780\pi$
$617$	206.947	−	206.947i	0.335409	−	0.335409i	0.854636	+	0.519227i	$0.173780\pi$
$618$	−0.366750	−	0.366750i	−0.000593447	−	0.000593447i
$619$		−	471.924i		−	0.762397i	−0.924493	−	0.381199i	$-0.875511\pi$
$619$		−	471.924i		−	0.762397i	0.924493	−	0.381199i	$-0.124489\pi$
$620$	222.198	+	86.6516i	0.358384	+	0.139761i
$621$	−607.048			−0.977532
$622$	439.079	−	439.079i	0.705915	−	0.705915i
$623$		0			0
$624$			110.734i			0.177458i
$625$	52.1015	+	622.825i	0.0833624	+	0.996519i
$626$	−294.243			−0.470037
$627$	7.62531	−	7.62531i	0.0121616	−	0.0121616i
$628$	225.282	+	225.282i	0.358730	+	0.358730i
$629$			883.865i			1.40519i
$630$		0			0
$631$	−675.457			−1.07045			−0.535227	−	0.844708i	$-0.679774\pi$
$631$	−675.457			−1.07045			−0.535227	+	0.844708i	$0.679774\pi$
$632$	224.533	−	224.533i	0.355274	−	0.355274i
$633$	131.815	+	131.815i	0.208239	+	0.208239i
$634$			583.346i			0.920104i
$635$	−307.135	−	699.823i	−0.483677	−	1.10208i
$636$	−305.599			−0.480502
$637$		0			0
$638$	−11.2982	−	11.2982i	−0.0177088	−	0.0177088i
$639$		−	399.631i		−	0.625400i
$640$	51.7995	−	22.7335i	0.0809367	−	0.0355211i
$641$	43.4962			0.0678568			0.0339284	−	0.999424i	$-0.489198\pi$
$641$	43.4962			0.0678568			0.0339284	+	0.999424i	$0.489198\pi$
$642$	220.446	−	220.446i	0.343374	−	0.343374i
$643$	344.145	+	344.145i	0.535218	+	0.535218i	0.922121	−	0.386902i	$-0.126455\pi$
$643$	344.145	+	344.145i	0.535218	+	0.535218i	−0.386902	+	0.922121i	$0.626455\pi$
$644$		0			0
$645$	443.707	+	173.035i	0.687918	+	0.268271i
$646$	−458.380			−0.709567
$647$	−658.101	+	658.101i	−1.01716	+	1.01716i	−0.0173069	+	0.999850i	$0.505509\pi$
$647$	−658.101	+	658.101i	−1.01716	+	1.01716i	−0.999850	+	0.0173069i	$0.994491\pi$
$648$	−31.4987	−	31.4987i	−0.0486092	−	0.0486092i
$649$		−	15.7861i		−	0.0243238i
$650$	−439.749	−	404.499i	−0.676537	−	0.622306i
$651$		0			0
$652$	353.045	−	353.045i	0.541480	−	0.541480i
$653$	−411.142	−	411.142i	−0.629621	−	0.629621i	0.318352	−	0.947973i	$-0.396871\pi$
$653$	−411.142	−	411.142i	−0.629621	−	0.629621i	−0.947973	+	0.318352i	$0.896871\pi$
$654$		−	118.417i		−	0.181066i
$655$	−106.970	+	274.299i	−0.163313	+	0.418778i
$656$	−0.802010			−0.00122258
$657$	210.398	−	210.398i	0.320241	−	0.320241i
$658$		0			0
$659$		−	217.266i		−	0.329691i	−0.986319	−	0.164846i	$-0.947287\pi$
$659$		−	217.266i		−	0.329691i	0.986319	−	0.164846i	$-0.0527126\pi$
$660$	4.49874	+	10.2506i	0.00681628	+	0.0155313i
$661$	123.739			0.187199			0.0935995	−	0.995610i	$-0.470163\pi$
$661$	123.739			0.187199			0.0935995	+	0.995610i	$0.470163\pi$
$662$	373.380	−	373.380i	0.564018	−	0.564018i
$663$	658.631	+	658.631i	0.993410	+	0.993410i
$664$			92.4645i			0.139254i
$665$		0			0
$666$	234.665			0.352350
$667$	282.850	−	282.850i	0.424062	−	0.424062i
$668$	405.599	+	405.599i	0.607184	+	0.607184i
$669$		−	368.148i		−	0.550296i
$670$	−9.24269	−	3.60442i	−0.0137951	−	0.00537973i
$671$	−8.31411			−0.0123906
$672$		0			0
$673$	−129.111	−	129.111i	−0.191844	−	0.191844i	0.604648	−	0.796493i	$-0.293314\pi$
$673$	−129.111	−	129.111i	−0.191844	−	0.191844i	−0.796493	+	0.604648i	$0.793314\pi$
$674$			518.032i			0.768593i
$675$	−626.708	+	26.1675i	−0.928457	+	0.0387667i
$676$	233.198			0.344967
$677$	311.789	−	311.789i	0.460545	−	0.460545i	−0.438289	−	0.898834i	$-0.644415\pi$
$677$	311.789	−	311.789i	0.460545	−	0.460545i	0.898834	+	0.438289i	$0.144415\pi$
$678$	−147.916	−	147.916i	−0.218165	−	0.218165i
$679$		0			0
$680$	172.881	−	443.314i	0.254237	−	0.651933i
$681$	−467.628			−0.686679
$682$	−16.2982	+	16.2982i	−0.0238977	+	0.0238977i
$683$	−35.2218	−	35.2218i	−0.0515692	−	0.0515692i	0.680852	−	0.732421i	$-0.261610\pi$
$683$	−35.2218	−	35.2218i	−0.0515692	−	0.0515692i	−0.732421	+	0.680852i	$0.761610\pi$
$684$			121.699i			0.177923i
$685$	264.772	+	603.297i	0.386528	+	0.880726i
$686$		0			0
$687$	−362.955	+	362.955i	−0.528319	+	0.528319i
$688$	164.464	+	164.464i	0.239047	+	0.239047i
$689$			1576.38i			2.28792i
$690$	−256.623	+	112.625i	−0.371917	+	0.163225i
$691$	327.950			0.474602			0.237301	−	0.971436i	$-0.423737\pi$
$691$	327.950			0.474602			0.237301	+	0.971436i	$0.423737\pi$
$692$	−22.1479	+	22.1479i	−0.0320056	+	0.0320056i
$693$		0			0
$694$			468.444i			0.674991i
$695$	−317.847	−	123.952i	−0.457334	−	0.178349i
$696$	−76.6015			−0.110060
$697$	−4.77027	+	4.77027i	−0.00684400	+	0.00684400i
$698$	383.298	+	383.298i	0.549138	+	0.549138i
$699$			82.8789i			0.118568i
$700$		0			0
$701$	−85.2715			−0.121643			−0.0608213	−	0.998149i	$-0.519372\pi$
$701$	−85.2715			−0.121643			−0.0608213	+	0.998149i	$0.519372\pi$
$702$	424.016	−	424.016i	0.604011	−	0.604011i
$703$	−178.939	−	178.939i	−0.254537	−	0.254537i
$704$			5.46700i			0.00776563i
$705$	142.210	−	364.664i	0.201716	−	0.517254i
$706$	788.749			1.11721
$707$		0			0
$708$	−53.5146	−	53.5146i	−0.0755856	−	0.0755856i
$709$			214.515i			0.302559i	0.988491	+	0.151280i	$0.0483394\pi$
$709$			214.515i			0.302559i	−0.988491	+	0.151280i	$0.951661\pi$
$710$	−179.784	−	409.647i	−0.253216	−	0.576967i
$711$	−709.145			−0.997391
$712$	159.699	−	159.699i	0.224297	−	0.224297i
$713$	−408.024	−	408.024i	−0.572263	−	0.572263i
$714$		0			0
$715$	52.8759	−	23.2059i	0.0739524	−	0.0324558i
$716$	685.799			0.957821
$717$	226.253	−	226.253i	0.315555	−	0.315555i
$718$	220.166	+	220.166i	0.306638	+	0.306638i
$719$			981.423i			1.36498i	0.730894	+	0.682491i	$0.239104\pi$
$719$			981.423i			1.36498i	−0.730894	+	0.682491i	$0.760896\pi$
$720$	−117.699	−	45.8997i	−0.163471	−	0.0637497i
$721$		0			0
$722$	−268.201	+	268.201i	−0.371469	+	0.371469i
$723$	107.644	+	107.644i	0.148885	+	0.148885i
$724$			176.264i			0.243459i
$725$	279.818	−	304.203i	0.385956	−	0.419590i
$726$	279.230			0.384614
$727$	10.5831	−	10.5831i	0.0145573	−	0.0145573i	−0.699791	−	0.714348i	$-0.746723\pi$
$727$	10.5831	−	10.5831i	0.0145573	−	0.0145573i	0.714348	+	0.699791i	$0.246723\pi$
$728$		0			0
$729$		−	270.419i		−	0.370946i
$730$	121.019	−	310.325i	0.165779	−	0.425102i
$731$	1956.43			2.67638
$732$	−28.1846	+	28.1846i	−0.0385036	+	0.0385036i
$733$	−769.238	−	769.238i	−1.04944	−	1.04944i	−0.998713	−	0.0507248i	$-0.983847\pi$
$733$	−769.238	−	769.238i	−1.04944	−	1.04944i	−0.0507248	−	0.998713i	$-0.516153\pi$
$734$			693.847i			0.945296i
$735$		0			0
$736$	−136.865			−0.185959
$737$	0.677952	−	0.677952i	0.000919881	−	0.000919881i
$738$	1.26650	+	1.26650i	0.00171612	+	0.00171612i
$739$		−	368.699i		−	0.498916i	−0.968386	−	0.249458i	$-0.919747\pi$
$739$		−	368.699i		−	0.498916i	0.968386	−	0.249458i	$-0.0802525\pi$
$740$	240.546	−	105.570i	0.325063	−	0.142662i
$741$	−266.681			−0.359893
$742$		0			0
$743$	−45.4536	−	45.4536i	−0.0611758	−	0.0611758i	0.675857	−	0.737033i	$-0.263774\pi$
$743$	−45.4536	−	45.4536i	−0.0611758	−	0.0611758i	−0.737033	+	0.675857i	$0.763774\pi$
$744$			110.501i			0.148523i
$745$	−407.363	−	158.861i	−0.546796	−	0.213237i
$746$	−61.9892			−0.0830954
$747$	146.016	−	146.016i	0.195470	−	0.195470i
$748$	32.5171	+	32.5171i	0.0434721	+	0.0434721i
$749$		0			0
$750$	−260.079	+	127.335i	−0.346772	+	0.169780i
$751$	784.546			1.04467			0.522334	−	0.852741i	$-0.325061\pi$
$751$	784.546			1.04467			0.522334	+	0.852741i	$0.325061\pi$
$752$	135.166	−	135.166i	0.179742	−	0.179742i
$753$	−385.330	−	385.330i	−0.511726	−	0.511726i
$754$			395.135i			0.524051i
$755$	428.690	−	1099.28i	0.567801	−	1.45599i
$756$		0			0
$757$	−535.185	+	535.185i	−0.706981	+	0.706981i	−0.965899	−	0.258918i	$-0.916634\pi$
$757$	−535.185	+	535.185i	−0.706981	+	0.706981i	0.258918	+	0.965899i	$0.416634\pi$
$758$	−393.135	−	393.135i	−0.518647	−	0.518647i
$759$		−	27.0844i		−	0.0356843i
$760$	54.7494	+	124.749i	0.0720386	+	0.164144i
$761$	−88.9632			−0.116903			−0.0584515	−	0.998290i	$-0.518616\pi$
$761$	−88.9632			−0.116903			−0.0584515	+	0.998290i	$0.518616\pi$
$762$	250.385	−	250.385i	0.328589	−	0.328589i
$763$		0			0
$764$			94.1688i			0.123258i
$765$	−973.069	+	427.056i	−1.27199	+	0.558243i
$766$	−168.749			−0.220299
$767$	−276.045	+	276.045i	−0.359902	+	0.359902i
$768$	18.5330	+	18.5330i	0.0241315	+	0.0241315i
$769$		−	999.457i		−	1.29968i	−0.760069	−	0.649842i	$-0.774835\pi$
$769$		−	999.457i		−	1.29968i	0.760069	−	0.649842i	$-0.225165\pi$
$770$		0			0
$771$	167.702			0.217512
$772$	−144.749	+	144.749i	−0.187499	+	0.187499i
$773$	254.153	+	254.153i	0.328788	+	0.328788i	0.852126	−	0.523337i	$-0.175313\pi$
$773$	254.153	+	254.153i	0.328788	+	0.328788i	−0.523337	+	0.852126i	$0.675313\pi$
$774$		−	519.430i		−	0.671098i
$775$	−438.827	−	403.650i	−0.566228	−	0.520839i
$776$	−202.734			−0.261255
$777$		0			0
$778$	426.710	+	426.710i	0.548471	+	0.548471i
$779$		−	1.93149i		−	0.00247945i
$780$	100.581	−	257.916i	0.128950	−	0.330661i
$781$	43.2348			0.0553582
$782$	−814.061	+	814.061i	−1.04100	+	1.04100i
$783$	293.319	+	293.319i	0.374609	+	0.374609i
$784$		0			0
$785$	−320.091	−	729.345i	−0.407759	−	0.929101i
$786$	−136.412			−0.173552
$787$	−56.2795	+	56.2795i	−0.0715114	+	0.0715114i	−0.741958	−	0.670446i	$-0.766103\pi$
$787$	−56.2795	+	56.2795i	−0.0715114	+	0.0715114i	0.670446	+	0.741958i	$0.266103\pi$
$788$	−326.296	−	326.296i	−0.414081	−	0.414081i
$789$			327.549i			0.415144i
$790$	−726.919	+	319.026i	−0.920150	+	0.403831i
$791$		0			0
$792$	8.63325	−	8.63325i	0.0109006	−	0.0109006i
$793$	145.385	+	145.385i	0.183336	+	0.183336i
$794$		−	155.282i		−	0.195570i
$795$	711.788	+	277.579i	0.895331	+	0.349156i
$796$	−681.462			−0.856108
$797$	−320.109	+	320.109i	−0.401642	+	0.401642i	−0.878811	−	0.477169i	$-0.841663\pi$
$797$	−320.109	+	320.109i	−0.401642	+	0.401642i	0.477169	+	0.878811i	$0.341663\pi$
$798$		0			0
$799$		−	1607.91i		−	2.01240i
$800$	−141.298	+	5.89975i	−0.176623	+	0.00737469i
$801$	−504.380			−0.629688
$802$	−78.8997	+	78.8997i	−0.0983787	+	0.0983787i
$803$	22.7623	+	22.7623i	0.0283466	+	0.0283466i
$804$		−	4.59648i		−	0.00571702i
$805$		0			0
$806$	570.000			0.707196
$807$	265.541	−	265.541i	0.329047	−	0.329047i
$808$	−110.000	−	110.000i	−0.136139	−	0.136139i
$809$			1156.40i			1.42942i	0.699422	+	0.714709i	$0.253441\pi$
$809$			1156.40i			1.42942i	−0.699422	+	0.714709i	$0.746559\pi$
$810$	44.7548	+	101.976i	0.0552528	+	0.125897i
$811$	−143.794			−0.177305			−0.0886526	−	0.996063i	$-0.528256\pi$
$811$	−143.794			−0.177305			−0.0886526	+	0.996063i	$0.528256\pi$
$812$		0			0
$813$	65.0764	+	65.0764i	0.0800448	+	0.0800448i
$814$			25.3876i			0.0311888i
$815$	−1142.97	+	501.622i	−1.40242	+	0.615487i
$816$	220.464			0.270177
$817$	−396.082	+	396.082i	−0.484800	+	0.484800i
$818$	−393.544	−	393.544i	−0.481105	−	0.481105i
$819$		0			0
$820$	1.86801	+	0.728476i	0.00227806	+	0.000888385i
$821$	−508.024			−0.618787			−0.309394	−	0.950934i	$-0.600126\pi$
$821$	−508.024			−0.618787			−0.309394	+	0.950934i	$0.600126\pi$
$822$	−215.850	+	215.850i	−0.262591	+	0.262591i
$823$	−1029.47	−	1029.47i	−1.25087	−	1.25087i	−0.955328	−	0.295546i	$-0.904498\pi$
$823$	−1029.47	−	1029.47i	−1.25087	−	1.25087i	−0.295546	−	0.955328i	$-0.595502\pi$
$824$			0.633250i			0.000768507i
$825$	−1.16750	−	27.9616i	−0.00141516	−	0.0338928i
$826$		0			0
$827$	−969.412	+	969.412i	−1.17220	+	1.17220i	−0.190520	+	0.981683i	$0.561017\pi$
$827$	−969.412	+	969.412i	−1.17220	+	1.17220i	−0.981683	+	0.190520i	$0.938983\pi$
$828$	216.132	+	216.132i	0.261029	+	0.261029i
$829$			863.253i			1.04132i	0.853765	+	0.520659i	$0.174314\pi$
$829$			863.253i			1.04132i	−0.853765	+	0.520659i	$0.825686\pi$
$830$	83.9866	−	215.364i	0.101189	−	0.259475i
$831$	−139.016			−0.167287
$832$	95.5990	−	95.5990i	0.114903	−	0.114903i
$833$		0			0
$834$		−	158.069i		−	0.189531i
$835$	−576.293	−	1313.11i	−0.690171	−	1.57259i
$836$	−13.1662			−0.0157491
$837$	423.127	−	423.127i	0.505528	−	0.505528i
$838$	−165.330	−	165.330i	−0.197291	−	0.197291i
$839$		−	541.425i		−	0.645322i	−0.946515	−	0.322661i	$-0.895423\pi$
$839$		−	541.425i		−	0.645322i	0.946515	−	0.322661i	$-0.104577\pi$
$840$		0			0
$841$	567.660			0.674982
$842$	−163.631	+	163.631i	−0.194336	+	0.194336i
$843$	157.763	+	157.763i	0.187144	+	0.187144i
$844$		−	227.599i		−	0.269667i
$845$	−543.155	−	211.817i	−0.642786	−	0.250671i
$846$	−426.897			−0.504607
$847$		0			0
$848$	263.831	+	263.831i	0.311122	+	0.311122i
$849$			515.312i			0.606963i
$850$	−805.335	+	875.518i	−0.947453	+	1.03002i
$851$	−635.576			−0.746857
$852$	146.565	−	146.565i	0.172024	−	0.172024i
$853$	203.211	+	203.211i	0.238231	+	0.238231i	0.816117	−	0.577886i	$-0.196122\pi$
$853$	203.211	+	203.211i	0.238231	+	0.238231i	−0.577886	+	0.816117i	$0.696122\pi$
$854$		0			0
$855$	110.541	−	283.457i	0.129288	−	0.331528i
$856$	−380.633			−0.444665
$857$	829.882	−	829.882i	0.968357	−	0.968357i	−0.0311577	−	0.999514i	$-0.509919\pi$
$857$	829.882	−	829.882i	0.968357	−	0.968357i	0.999514	+	0.0311577i	$0.00991941\pi$
$858$	18.9181	+	18.9181i	0.0220491	+	0.0220491i
$859$		−	294.203i		−	0.342495i	−0.985228	−	0.171247i	$-0.945220\pi$
$859$		−	294.203i		−	0.342495i	0.985228	−	0.171247i	$-0.0547797\pi$
$860$	−233.678	−	532.449i	−0.271719	−	0.619126i
$861$		0			0
$862$	−419.744	+	419.744i	−0.486942	+	0.486942i
$863$	−1003.37	−	1003.37i	−1.16266	−	1.16266i	−0.983892	−	0.178764i	$-0.942790\pi$
$863$	−1003.37	−	1003.37i	−1.16266	−	1.16266i	−0.178764	−	0.983892i	$-0.557210\pi$
$864$		−	141.931i		−	0.164273i
$865$	71.7030	−	31.4687i	0.0828937	−	0.0363799i
$866$	711.900			0.822055
$867$	976.546	−	976.546i	1.12635	−	1.12635i
$868$		0			0
$869$		−	76.7201i		−	0.0882855i
$870$	178.417	+	69.5781i	0.205077	+	0.0799748i
$871$	−23.7101			−0.0272217
$872$	−102.232	+	102.232i	−0.117239	+	0.117239i
$873$	320.148	+	320.148i	0.366721	+	0.366721i
$874$		−	329.615i		−	0.377134i
$875$		0			0
$876$	154.327			0.176173
$877$	990.122	−	990.122i	1.12899	−	1.12899i	0.138645	−	0.990342i	$-0.455725\pi$
$877$	990.122	−	990.122i	1.12899	−	1.12899i	0.990342	−	0.138645i	$-0.0442746\pi$
$878$	187.765	+	187.765i	0.213856	+	0.213856i
$879$		−	427.879i		−	0.486779i
$880$	4.96575	−	12.7335i	0.00564289	−	0.0144699i
$881$	1069.93			1.21445			0.607223	−	0.794532i	$-0.292284\pi$
$881$	1069.93			1.21445			0.607223	+	0.794532i	$0.292284\pi$
$882$		0			0
$883$	1198.71	+	1198.71i	1.35754	+	1.35754i	0.876944	+	0.480593i	$0.159579\pi$
$883$	1198.71	+	1198.71i	1.35754	+	1.35754i	0.480593	+	0.876944i	$0.340421\pi$
$884$		−	1137.22i		−	1.28645i
$885$	76.0359	+	173.252i	0.0859163	+	0.195765i
$886$	−846.143			−0.955014
$887$	−54.5301	+	54.5301i	−0.0614770	+	0.0614770i	−0.737177	−	0.675700i	$-0.763842\pi$
$887$	−54.5301	+	54.5301i	−0.0614770	+	0.0614770i	0.675700	+	0.737177i	$0.263842\pi$
$888$	86.0635	+	86.0635i	0.0969183	+	0.0969183i
$889$		0			0
$890$	−517.021	+	226.908i	−0.580923	+	0.254952i
$891$	−10.7627			−0.0120794
$892$	−317.831	+	317.831i	−0.356313	+	0.356313i
$893$	325.523	+	325.523i	0.364527	+	0.364527i
$894$		−	202.586i		−	0.226606i
$895$	−1597.33	−	622.920i	−1.78473	−	0.696000i
$896$		0			0
$897$	−473.612	+	473.612i	−0.527996	+	0.527996i
$898$	−93.8630	−	93.8630i	−0.104524	−	0.104524i
$899$			394.306i			0.438605i
$900$	232.449	+	213.815i	0.258276	+	0.237573i
$901$	3138.48			3.48333
$902$	−0.137018	+	0.137018i	−0.000151905	+	0.000151905i
$903$		0			0
$904$			255.398i			0.282520i
$905$	160.103	−	410.546i	0.176909	−	0.453642i
$906$	546.681			0.603401
$907$	712.955	−	712.955i	0.786059	−	0.786059i	−0.194787	−	0.980846i	$-0.562402\pi$
$907$	712.955	−	712.955i	0.786059	−	0.786059i	0.980846	+	0.194787i	$0.0624015\pi$
$908$	403.715	+	403.715i	0.444620	+	0.444620i
$909$			347.414i			0.382194i
$910$		0			0
$911$	−1241.02			−1.36226			−0.681130	−	0.732162i	$-0.738511\pi$
$911$	−1241.02			−1.36226			−0.681130	+	0.732162i	$0.738511\pi$
$912$	−44.6332	+	44.6332i	−0.0489400	+	0.0489400i
$913$	15.7970	+	15.7970i	0.0173023	+	0.0173023i
$914$			299.884i			0.328101i
$915$	91.2469	−	40.0460i	0.0997233	−	0.0437661i
$916$	626.697			0.684167
$917$		0			0
$918$	−844.193	−	844.193i	−0.919600	−	0.919600i
$919$			6.73601i			0.00732972i	0.999993	+	0.00366486i	$0.00116656\pi$
$919$			6.73601i			0.00732972i	−0.999993	+	0.00366486i	$0.998833\pi$
$920$	318.781	+	124.317i	0.346501	+	0.135127i
$921$	−858.649			−0.932301
$922$	−350.396	+	350.396i	−0.380039	+	0.380039i
$923$	−756.027	−	756.027i	−0.819097	−	0.819097i
$924$		0			0
$925$	−656.160	+	27.3972i	−0.709363	+	0.0296186i
$926$	654.760			0.707084
$927$	1.00000	−	1.00000i	0.00107875	−	0.00107875i
$928$	66.1320	+	66.1320i	0.0712629	+	0.0712629i
$929$		−	417.348i		−	0.449245i	−0.974446	−	0.224622i	$-0.927885\pi$
$929$		−	417.348i		−	0.449245i	0.974446	−	0.224622i	$-0.0721149\pi$
$930$	100.370	−	257.375i	0.107924	−	0.276747i
$931$		0			0
$932$	71.5514	−	71.5514i	0.0767719	−	0.0767719i
$933$	−508.591	−	508.591i	−0.545114	−	0.545114i
$934$			769.378i			0.823745i
$935$	−46.2018	−	105.273i	−0.0494136	−	0.112592i
$936$	−301.931			−0.322576
$937$	−46.4937	+	46.4937i	−0.0496198	+	0.0496198i	−0.731481	−	0.681862i	$-0.761171\pi$
$937$	−46.4937	+	46.4937i	−0.0496198	+	0.0496198i	0.681862	+	0.731481i	$0.261171\pi$
$938$		0			0
$939$			340.825i			0.362966i
$940$	−437.596	+	192.050i	−0.465528	+	0.204309i
$941$	−1440.88			−1.53123			−0.765614	−	0.643301i	$-0.777564\pi$
$941$	−1440.88			−1.53123			−0.765614	+	0.643301i	$0.777564\pi$
$942$	260.947	−	260.947i	0.277014	−	0.277014i
$943$	−3.43023	−	3.43023i	−0.00363758	−	0.00363758i
$944$			92.4010i			0.0978824i
$945$		0			0
$946$	56.1955			0.0594033
$947$	395.249	−	395.249i	0.417369	−	0.417369i	−0.466927	−	0.884296i	$-0.654639\pi$
$947$	395.249	−	395.249i	0.417369	−	0.417369i	0.884296	+	0.466927i	$0.154639\pi$
$948$	−260.079	−	260.079i	−0.274345	−	0.274345i
$949$		−	796.069i		−	0.838851i
$950$	−14.2084	−	340.290i	−0.0149563	−	0.358200i
$951$	675.697			0.710512
$952$		0			0
$953$	27.0794	+	27.0794i	0.0284149	+	0.0284149i	0.721171	−	0.692757i	$-0.243604\pi$
$953$	27.0794	+	27.0794i	0.0284149	+	0.0284149i	−0.692757	+	0.721171i	$0.743604\pi$
$954$		−	833.261i		−	0.873440i
$955$	85.5347	−	219.334i	0.0895651	−	0.229669i
$956$	−390.660			−0.408640
$957$	−13.0869	+	13.0869i	−0.0136749	+	0.0136749i
$958$	−67.6332	−	67.6332i	−0.0705984	−	0.0705984i
$959$		0			0
$960$	−26.3325	−	60.0000i	−0.0274297	−	0.0625000i
$961$	−392.195			−0.408112
$962$	443.942	−	443.942i	0.461479	−	0.461479i
$963$	601.079	+	601.079i	0.624174	+	0.624174i
$964$		−	185.863i		−	0.192804i
$965$	468.622	−	205.666i	0.485618	−	0.213126i
$966$		0			0
$967$	1012.58	−	1012.58i	1.04713	−	1.04713i	0.0483007	−	0.998833i	$-0.484619\pi$
$967$	1012.58	−	1012.58i	1.04713	−	1.04713i	0.998833	−	0.0483007i	$-0.0153806\pi$
$968$	−241.066	−	241.066i	−0.249035	−	0.249035i
$969$			530.947i			0.547933i
$970$	472.198	+	184.145i	0.486802	+	0.189841i
$971$	−1353.35			−1.39377			−0.696884	−	0.717184i	$-0.745431\pi$
$971$	−1353.35			−1.39377			−0.696884	+	0.717184i	$0.745431\pi$
$972$	−355.831	+	355.831i	−0.366082	+	0.366082i
$973$		0			0
$974$		−	1054.34i		−	1.08249i
$975$	−468.536	+	509.367i	−0.480550	+	0.522428i
$976$	48.6650			0.0498617
$977$	438.436	−	438.436i	0.448757	−	0.448757i	−0.446184	−	0.894941i	$-0.647217\pi$
$977$	438.436	−	438.436i	0.448757	−	0.448757i	0.894941	+	0.446184i	$0.147217\pi$
$978$	−408.937	−	408.937i	−0.418135	−	0.418135i
$979$		−	54.5673i		−	0.0557377i
$980$		0			0
$981$	322.881			0.329135
$982$	−199.061	+	199.061i	−0.202710	+	0.202710i
$983$	−948.889	−	948.889i	−0.965299	−	0.965299i	0.0341184	−	0.999418i	$-0.489138\pi$
$983$	−948.889	−	948.889i	−0.965299	−	0.965299i	−0.999418	+	0.0341184i	$0.989138\pi$
$984$			0.928978i			0.000944084i
$985$	463.615	+	1056.37i	0.470675	+	1.07246i
$986$	786.692			0.797862
$987$		0			0
$988$	230.232	+	230.232i	0.233029	+	0.233029i
$989$			1406.84i			1.42249i
$990$	−27.9499	+	12.2665i	−0.0282322	+	0.0123904i
$991$	1455.69			1.46891			0.734453	−	0.678660i	$-0.237439\pi$
$991$	1455.69			1.46891			0.734453	+	0.678660i	$0.237439\pi$
$992$	95.3985	−	95.3985i	0.0961678	−	0.0961678i
$993$	−432.491	−	432.491i	−0.435540	−	0.435540i
$994$		0			0
$995$	1587.23	+	618.980i	1.59521	+	0.622091i
$996$	107.103			0.107533
$997$	648.193	−	648.193i	0.650143	−	0.650143i	−0.302884	−	0.953027i	$-0.597950\pi$
$997$	648.193	−	648.193i	0.650143	−	0.650143i	0.953027	+	0.302884i	$0.0979496\pi$
$998$	−544.799	−	544.799i	−0.545891	−	0.545891i
$999$		−	659.101i		−	0.659761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.f.393.2		4
5.2	odd	4	inner	490.3.f.f.197.2		4
7.2	even	3		70.3.l.b.53.1	yes	8
7.4	even	3		70.3.l.b.23.2	✓	8
7.6	odd	2		490.3.f.k.393.1		4
35.2	odd	12		70.3.l.b.67.2	yes	8
35.4	even	6		350.3.p.b.93.1		8
35.9	even	6		350.3.p.b.193.2		8
35.18	odd	12		350.3.p.b.107.2		8
35.23	odd	12		350.3.p.b.207.1		8
35.27	even	4		490.3.f.k.197.1		4
35.32	odd	12		70.3.l.b.37.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.b.23.2	✓	8	7.4	even	3
70.3.l.b.37.1	yes	8	35.32	odd	12
70.3.l.b.53.1	yes	8	7.2	even	3
70.3.l.b.67.2	yes	8	35.2	odd	12
350.3.p.b.93.1		8	35.4	even	6
350.3.p.b.107.2		8	35.18	odd	12
350.3.p.b.193.2		8	35.9	even	6
350.3.p.b.207.1		8	35.23	odd	12
490.3.f.f.197.2		4	5.2	odd	4	inner
490.3.f.f.393.2		4	1.1	even	1	trivial
490.3.f.k.197.1		4	35.27	even	4
490.3.f.k.393.1		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.15831 + 1.15831i) q^{3} -2.00000i q^{4} +(-1.81662 + 4.65831i) q^{5} -2.31662 q^{6} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.15831 + 1.15831i) q^{3} -2.00000i q^{4} +(-1.81662 + 4.65831i) q^{5} -2.31662 q^{6} +(2.00000 + 2.00000i) q^{8} -6.31662i q^{9} +(-2.84169 - 6.47494i) q^{10} +0.683375 q^{11} +(2.31662 - 2.31662i) q^{12} +(-11.9499 - 11.9499i) q^{13} +(-7.50000 + 3.29156i) q^{15} -4.00000 q^{16} +(-23.7916 + 23.7916i) q^{17} +(6.31662 + 6.31662i) q^{18} -9.63325i q^{19} +(9.31662 + 3.63325i) q^{20} +(-0.683375 + 0.683375i) q^{22} +(-17.1082 - 17.1082i) q^{23} +4.63325i q^{24} +(-18.3997 - 16.9248i) q^{25} +23.8997 q^{26} +(17.7414 - 17.7414i) q^{27} +16.5330i q^{29} +(4.20844 - 10.7916i) q^{30} +23.8496 q^{31} +(4.00000 - 4.00000i) q^{32} +(0.791562 + 0.791562i) q^{33} -47.5831i q^{34} -12.6332 q^{36} +(18.5752 - 18.5752i) q^{37} +(9.63325 + 9.63325i) q^{38} -27.6834i q^{39} +(-12.9499 + 5.68338i) q^{40} +0.200503 q^{41} +(-41.1161 - 41.1161i) q^{43} -1.36675i q^{44} +(29.4248 + 11.4749i) q^{45} +34.2164 q^{46} +(-33.7916 + 33.7916i) q^{47} +(-4.63325 - 4.63325i) q^{48} +(35.3246 - 1.47494i) q^{50} -55.1161 q^{51} +(-23.8997 + 23.8997i) q^{52} +(-65.9578 - 65.9578i) q^{53} +35.4829i q^{54} +(-1.24144 + 3.18338i) q^{55} +(11.1583 - 11.1583i) q^{57} +(-16.5330 - 16.5330i) q^{58} -23.1003i q^{59} +(6.58312 + 15.0000i) q^{60} -12.1662 q^{61} +(-23.8496 + 23.8496i) q^{62} +8.00000i q^{64} +(77.3747 - 33.9578i) q^{65} -1.58312 q^{66} +(0.992064 - 0.992064i) q^{67} +(47.5831 + 47.5831i) q^{68} -39.6332i q^{69} +63.2665 q^{71} +(12.6332 - 12.6332i) q^{72} +(33.3087 + 33.3087i) q^{73} +37.1504i q^{74} +(-1.70844 - 40.9169i) q^{75} -19.2665 q^{76} +(27.6834 + 27.6834i) q^{78} -112.266i q^{79} +(7.26650 - 18.6332i) q^{80} -15.7494 q^{81} +(-0.200503 + 0.200503i) q^{82} +(23.1161 + 23.1161i) q^{83} +(-67.6082 - 154.049i) q^{85} +82.2322 q^{86} +(-19.1504 + 19.1504i) q^{87} +(1.36675 + 1.36675i) q^{88} -79.8496i q^{89} +(-40.8997 + 17.9499i) q^{90} +(-34.2164 + 34.2164i) q^{92} +(27.6253 + 27.6253i) q^{93} -67.5831i q^{94} +(44.8747 + 17.5000i) q^{95} +9.26650 q^{96} +(-50.6834 + 50.6834i) q^{97} -4.31662i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 6 q^{5} + 4 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 6 * q^5 + 4 * q^6 + 8 * q^8	\( 4 q - 4 q^{2} - 2 q^{3} + 6 q^{5} + 4 q^{6} + 8 q^{8} - 18 q^{10} + 16 q^{11} - 4 q^{12} - 8 q^{13} - 30 q^{15} - 16 q^{16} - 62 q^{17} + 12 q^{18} + 24 q^{20} - 16 q^{22} - 22 q^{23} + 6 q^{25} + 16 q^{26} - 2 q^{27} + 50 q^{30} - 24 q^{31} + 16 q^{32} - 30 q^{33} - 24 q^{36} + 134 q^{37} + 12 q^{38} - 12 q^{40} + 160 q^{41} + 8 q^{43} + 58 q^{45} + 44 q^{46} - 102 q^{47} + 8 q^{48} + 2 q^{50} - 48 q^{51} - 16 q^{52} - 98 q^{53} + 68 q^{55} + 38 q^{57} + 40 q^{58} - 40 q^{60} + 84 q^{61} + 24 q^{62} + 210 q^{65} + 60 q^{66} + 130 q^{67} + 124 q^{68} + 200 q^{71} + 24 q^{72} + 246 q^{73} - 40 q^{75} - 24 q^{76} + 124 q^{78} - 24 q^{80} + 136 q^{81} - 160 q^{82} - 80 q^{83} - 224 q^{85} - 16 q^{86} - 196 q^{87} + 32 q^{88} - 84 q^{90} - 44 q^{92} + 210 q^{93} + 80 q^{95} - 16 q^{96} - 216 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 6 * q^5 + 4 * q^6 + 8 * q^8 - 18 * q^10 + 16 * q^11 - 4 * q^12 - 8 * q^13 - 30 * q^15 - 16 * q^16 - 62 * q^17 + 12 * q^18 + 24 * q^20 - 16 * q^22 - 22 * q^23 + 6 * q^25 + 16 * q^26 - 2 * q^27 + 50 * q^30 - 24 * q^31 + 16 * q^32 - 30 * q^33 - 24 * q^36 + 134 * q^37 + 12 * q^38 - 12 * q^40 + 160 * q^41 + 8 * q^43 + 58 * q^45 + 44 * q^46 - 102 * q^47 + 8 * q^48 + 2 * q^50 - 48 * q^51 - 16 * q^52 - 98 * q^53 + 68 * q^55 + 38 * q^57 + 40 * q^58 - 40 * q^60 + 84 * q^61 + 24 * q^62 + 210 * q^65 + 60 * q^66 + 130 * q^67 + 124 * q^68 + 200 * q^71 + 24 * q^72 + 246 * q^73 - 40 * q^75 - 24 * q^76 + 124 * q^78 - 24 * q^80 + 136 * q^81 - 160 * q^82 - 80 * q^83 - 224 * q^85 - 16 * q^86 - 196 * q^87 + 32 * q^88 - 84 * q^90 - 44 * q^92 + 210 * q^93 + 80 * q^95 - 16 * q^96 - 216 * q^97

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